DTIC ADA514737: Research Studies on Electromagnetically Induced Transparency

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3. DATES COVERED (From - To)
2. REPORT TYPE
REPORT DATE (DD-MM-YYYY)
1.
1 November, 2006 - 31 October, 2009
Final Performance Report
20-01-2010
5a. CONTRACT NUMBER
4. TITLE AND SUBTITLE
FA9550-07-1-0009
Research Studies on Electromagnetically Induced Transparency
5b. GRANT NUMBER
5c. PROGRAM ELEMENT NUMBER
5d. PROJECT NUMBER
6. AUTHOR(S)
S. E. Harris
5e. TASK NUMBER
5f. WORK UNIT NUMBER
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)
8. PERFORMING ORGANIZATION
REPORT NUMBER
Leland Stanford Junior University
651 Serra Street
Stanford, CA 94305-6215
10. SPONSOR/MONITORS ACRONYM(S)
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)
AF Office of Scientific Research (AFOSR)
875 North Randolph Street
Arlington, VA 22203-1768
11. SPONSOR/MONITORS REPORT
NUMBER(S)
12. DISTRIBUTION/AVAILABILITY STATEMENT
Unlimited.
20100303211
13. SUPPLEMENTARY NOTES
14. ABSTRACT
The overall theme of this work has been the development and utilization of new sources of radiation that produce time energy entangled biphotons
that are both much longer and much shorter than those that now exist. We have learned to produce biphotons with temporal lengths greater than
500 ns and linewidths smaller than the natural linewidth of target atoms. We have demonstrated the use of telecommunication light modulators to
modulate single photons and also a novel technique for measuring the temporal length of biphoton wave packets. The technique is based on the
use of synchronously driven fast modulators and slow detectors. By measuring the coincidence count rate between single photon counting modules
as a function of the sinusoidal modulation frequency we obtain the Fourier transform of the biphoton wave function. Accomplishments in the area
of ultra-short biphotons include the suggestion for using the method of chirp and compress at the single photon level, and the first demonstration of
resonance sum frequency generation with paired photons. We have demonstrated a new quantum effect that we term as nonlocal modulation were
phase modulators at distant locations, acting on the photons of an entangled pair, interfere to determine the apparent depth of modulation.
15. SUBJECT TERMS
electromagnetically induced transparency, photon interactions with atoms, nonclassical states of the electromagnetic field, including
entangled photon states, quantum engineering and measurements, parametric down conversion and production of entangled photons.
17. LIMITATION OF
16. SECURITY CLASSIFICATION OF: 18. NUMBER
19a. NAME OF RESPONSIBLE PERSON
ABSTRACT
OF
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93
Standard Form 298 (Rev. 8/98)
Prescribed by ANSI Std. Z39.18
Final Performance Report
RESEARCH STUDIES ON ELECTROMAGNETICALLY INDUCED
TRANSPARENCY
Grant AFOSR FA9550-07-1-0009
Prepared for
AIR FORCE OFFICE OF SCIENTIFIC RESEARCH
and
ARMY RESEARCH OFFICE
For the Period
November 1, 2007 to October 31, 2009
Submitted by
1
S. E. Harris , Principal Investigator
Edward L.Ginzton Laboratory
Stanford University
1
[email protected]
Contents

1 EXECUTIVE SUMMARY 2

2 Subnatural Linewidth Biphoton Generation with 2-D MOT 5

3 Theory of EIT- based Paired Photon Generation 10

4 Electro-Optic Modulation of Single Photons 11

5 Modulation and Measurement of Time-Energy Entangled Photons 16
6 Resonator Sum Frequency Generation with Time- Energy Entangled Pho-

tons 22

7 Observation of Nonlocal Modulation with Entangled Photons 29

8 Chirp and Compress with Biphotons 37

9 Nonlinear Optics at X-Ray Wavelengths 43

10 Joint Support 53

APPENDIX 54

A Publications During Grant Period 54

B Chirped Crystal Simulation Code 56

C Chapter 4 of Kolchin's Dissertation 64
1 EXECUTIVE SUMMARY
Our work during this contract period began with emphasis on electromagnetically induced
transparency, slow light, and its application to making ultra-long biphotons. As the program
evolved, we increased emphasis on novel techniques to produce, measure, and utilize both
long and short biphotons.
We begin by summarizing the key property of time-energy entangled biphotons. This is:
if an observer at point A chooses to measure the frequency of an arriving photon he will then
know to high accuracy the frequency of the photon which will be measured by an observer
at point B. But instead, if the observer at point A chooses to measure the time of arrival of
a photon at his location, he will then know, again to high accuracy, the time of arrival of
the photon at point B. The accuracy of these measurements is not limited by the Heisenberg
uncertainty principle.
We turn next to what is meant by long and short. Typical biphotons as generated by
nonlinear optical crystals have temporal lengths in the range of between 0.1 ps and 10 ps.
Such photons are not resolvable by presently existing photo detectors. These detectors,
measure whether or not a photon is present, but may not be used to examine the functional
form of the photonic wave packet.
By using the techniques of slow light and working under AFOSR-ARO and DARPA
support, in 2005 our group demonstrated the first method of generating temporally long
biphotons. The length of these photons is controlled by the group delay in the nonlinear
media and in early experiments resulted in photons with a length of about 40 ns. A key
accomplishment of the present program was the extension of this length to photons whose
length could be continuously varied from 50 to 900 ns. Of importance, the line width of
these photons was less than the natural linewidth of the rubidium vapor that was used
to produce them. This is important because optical nonlinearities when produced using
electromagnetically induced transparency continue to increase in the subnatural linewidth
regime and in the absence of dephasing may be made arbitrarily large. This should soon
allow the demonstration of nonlinear optics with single photons.
We mention a surprise that occurred during this work. In the course of observing long
biphotons with a length determined by the slow optical group velocities, we found that
the photonic wave packets had a sharp leading edge spike on their front edge. Following
a suggestion by Dan Gauthier we recognized that this front edge spike is a Sommerfeld-
Brillouin precursor. This observation is important because it clarifies, for both slow light
and fast light, that information will always be transmitted at the speed of light in vacuum.
In January 2008 we recognized that we had the capability to modulate single photons for
the first time. To do this we used the Stokes photon of a biphoton pair to set the time origin
for electro-optic modulation of the wave function of the anti-stokes photon. With the time
origin determined, the modulator could arbitrarily modulate either the amplitude or phase
of the anti-stokes photon. The technique therefore provides the technology for studying the
response of atoms to shaped single-photon waveforms on a time scale comparable to the
natural linewidth of target atoms.
The next step in our work in modulating biphotons was the development of a method for
measuring their length using slow detectors. The essential idea is that modulation in the time
domain followed by slow integration constitutes a Fourier transformation. The experimental
technique is to measure the coincidence count rate between single photon counting modules as
a function of an applied sinusoidal frequency. The inverse Fourier transform of the data then
yields the biphoton waveform. Though this experiment was a proof of principle experiment,
ultimately it could be used to measure wavepacket profile of biphotons when sufficiently fast
photo detectors are not available.
We are now working on an important extension of our work on modulating single pho-
tons. This is the application of spread spectrum techniques at the single photon level. Spread
spectrum is well known in the communications industry as a technique for avoiding inter-
ference and jamming, and at times increasing information capacity. Our work is the first
demonstration of this technique to single photons.
We turn next to our work on short biphotons. Our first contribution was a PRL entitled
Chirp and Compress : Toward Single-Cycle Biphotons. In this work we described a method
for generating time-energy entangled photons with a spectral width that exceeds an octave,
and of compressing their spectrum to produce biphotons whose temporal length is a single
optical cycle. The elements of the technique are the suggestion for using parametric down
conversion in a periodically poled material to spontaneously generate pairs of entangled
photons whose instantaneous frequencies are chirped in opposite directions and the use of
the non-local nature of entangled photons to allow the dispersion, as experienced by one
photon, to cancel out the dispersion of the second photon and to compress the biphoton
wave packet.
Our first experimental work in this area was the development of a novel resonant sum
frequency generation technique (PRL February 2009). This work demonstrates a rather
amazing effect where we take two single photons that each have a broad spectral linewidth
and sum them. We find that though each photon has a broad linewidth, the linewidth of
the sum frequency photon is as narrow as that of the pumping laser. Also, the output (sum)
power is linear rather than quadratic in input power. These effects both derive from the
quantum behavior of single photons.
In the course of studying nonlocal dispersion compensation as described above, we recog-
nized that there should be a new quantum effect that we have termed as nonlocal modulation.
Assume that single and idler photons pass through sinusoidal phase modulators located at
different locations. These modulators are driven at the same modulation frequency and are
connected by cable such that their relative phase may be varied. After passing through
the modulators the single and idler photons are dispersed, for example by a prism, and
the relative positions of the single and idler photons are correlated. We find : When the
modulators are run with the same phase the modulation depths add; when they are run in
phase opposition the modulation depths subtract. Two distant modulators with the same
modulation depth and opposite phase therefore have the same frequency correlation as when
both modulators are absent. This effect is entirely quantum mechanical. Mathematically
it results because, quantum mechanically, one adds probability amplitudes before squaring,
while classically one squares before adding.
As this contract ends, we are beginning work in the area on nonlinear and quantum optics
at x-ray wavelengths. To a great extent we are motivated by the new 1.5 Angstrom free
electron laser that is now operating at Stanford. We anticipate experiments to demonstrate
frequency doubling of this laser with the further objective of using SHG as a correlator and
diagnostic for the laser itself.
2 Subnatural Linewidth Biphoton Generation with 2-D
MOT
The most significant experimental advance in cold atom EIT research project during perfor-
mance period is that we observed subnatural linewidth biphotons with our MOT generation
II, which is our new platform for biphoton generation in a series of modulation studies at
single photon level. Figure 1 shows both experimental configuration (geometry) and mech-
anism of parametric paired-photon generation. In contrast to previous MOT constructed in
85
early grant period (W911NF-04-1-0105), the new 2-D Rb MOT has a cigar shaped atom
cloud(~1.7 cm long and an aspect ratio of 25) and consequently a large optical depth in the
(b)
(a)
SPCM
|4>5P (F=3)
W
|3)5P (F=3)
1/2
Figure 1: Upper: Biphoton generation in a double-A system, (a) Experimental configura-
85
tion. Fj and F2 are narrow-band optical frequency niters, (b) Rb energy level diagram.
In the presence of counter-propagating pump (u) ) and coupling (co ) beams, Stokes (u> )and
p c s
anti-Stokes, (u> ) photons are generated into opposing single-mode fibers. Lower: 2-D MOT
as
apparatus. The vacuum cell is 6 cm size ceramic structured octagon. The cell is located in
the middle of water cooled trapping coil(racetrack-shaped cage).
longitudinal direction; moreover, its cylindrical quadrupole trapping field results in minimal
longitudinal magnetic field gradient and hence greatly reduces the inhomogeneous Zeeman
broadening of the m-states of the 5S\/2 level. The experimental cycle comprises 4.5 ms of
trapping time and 0.5 ms paired photon generation window. At the end of the trapping
cycle, the rubidium cloud is prepared in 5S\/2 level by turning off the repumping laser 0.3
ms before turning off the trapping laser; counter-propagating, circularly polarized, cw pump
and coupling (u> ) lasers are subsequently turned on and phase-matched, paired Stokes
(UJ )
c
P
(u ) and anti-Stokes (uj ) photons are spontaneously generated and propagate in opposite
3 as
directions as shown in the figure.
Figure 2: Biphoton wave packet data for three slow group delay cases. The upper row plots
are anti-Stokes EIT scan data(o) and EIT fit (blue curve), the lower row plots are paired-
photon coincidence count data(+) and predicted wave packet shape with time bin width of 1
ns for 800 s(lower row). Propagation delay of anti-Stokes pulse(red traces in inserts of lower
row plots) are also presented for three slow group delay((r ) cases. Experimental parameters
9
are: Left: (r ~ 50ns) OD=7, fi = 4.207i , ftp = I.I6713, and A = 48.677i . Middle:
g c 3 p 3
{j ~ 320ns) OD=53, ft = 4.2O713, ftp = I.I6713, and A = 48.677 . Right: (r ~ 900ns)
g c p 13 9
OD=53, ft = 2.35713, ftp = I.I6713, and A = 48.677 .
c p 13
85
The optical depth of the 2-D Rb MOT can be varied up to 62, which gives us enough
parameter space to verify the relation between the optical group delay and the length of
the biphoton waveform. Figure 2 shows sets of anti-Stokes EIT scan and paired-photon
coincidence counts for three anti-Stokes EIT group delay cases, which is controlled by varying
2
the optical depth and the coupling laser power(r ~ (27i /|ft | )./V<TL, where NaL is the
9 3 c
optical depth and 713 is the dephasing rate of level |3)). The trapping laser used for these
experimental runs has a power of 160 mW, a beam diameter of 2 cm, and is red detuned by
20 MHz from the |5Si/2,.F = 3) —> |5P3/2,F = 4) transition. A repumping laser is locked
to the |5S!/2,.F = 2) —• |5P /2,-F = 2) transition, has a power of 80 mW, and overlaps one
3
2
of six trapping beams. The pump laser is circularly polarized (cr~), has a 1/e diameter of
1.46 mm, and is blue detuned from the |1) —> |4) transition by 146 MHz, i.e. A = 48.677i .
p 3
+ 2
The coupling laser is circularly polarized {(T ), has a 1/e beam diameter of 1.63 mm and
is on resonance with the |2) —» |3) transition. The counter-propagating pump and coupling
beams are collinear and set at a 2 degree angle from the longitudinal axis of the MOT. The
+
Stokes (a~) and anti-Stokes (a ) photons are coupled into opposing single mode fibers after
passage through A/4 wave plates and polarization beam splitters (PBS). The Stokes and
2
anti-Stokes fiber coupling efficiency is 70% and the 1/e waist diameter of their foci is 220
jirn.
p-
—i 1 1—
1000(4' " | i ' • | " i | i ' • | " '
1 • 1 -M
40000
" =4.20 y
c 13
• Experiment
— Theory
g 800 -
30000 -
n =2.35 „
c r
• Experiment
— Theory
£ 20000 -
•y
-
10000 -
I

Jf
i

i
2
i

S. I .
i

1 , 1 -r
) I I I I
60
200 400 600 800 1000 0 20 40
Group delay (ns)
Optical depth (OD)
Figure 3: (a) Measured correlation time vs measured anti-Stokes group delay. The solid line
is a linear least squares fit. (b) Paired counts in a 1 ns bin in 800 s as a function of the
optical depth.
As shown in Fig. 2, the temporal length of biphoton wavepacket generated in high OD case
are much longer(by more than one order) than previously reported in our phase I research.
It also means that the generated biphoton has much narrowed bandwidth. The predicted
biphoton packet waveforms in lower row plots of Fig. 2 are computed with all parameters
obtained from the EIT measurements and vertically scaled to fit the experimental data. The
calculated biphoton linewidths are 9.66, 2.36 and 0.75 MHz respectively. These linewidths
are comparable to the measured EIT bandwidths and in the latter two cases are less than
the 6 MHz natural linewidth of Rb D line. Thanks to the 2-D MOT, which is designed to
have increase in OD and decreases in dephasing, the biphoton generation now is in the linear
group delay regime where > r and the correlation width directly follows group delay time
T
r
9
as shown in data plot of Fig. 3(a).
Having taken into account the filter and etalon transmissions, the fiber to fiber coupling
efficiency, the detector quantum efficiencies and the duty cycle, for the conditions of Fig. 2,
we observe a total of 3213, 31674, and 22000 paired counts in 800 seconds, which correspond
8